# Give an example of a function f(x)

#### Alexmahone

##### Active member
Give an example of a function $\displaystyle f(x)$ for which $\displaystyle f([-1,\ 1])=(-\infty,\ \infty)$.

My thoughts: $\displaystyle f(x)=\frac{x}{(x-1)(x+1)}$ is a function for which $f((-1,\ 1))=(-\infty,\ \infty)$.

#### CaptainBlack

##### Well-known member
Give an example of a function $\displaystyle f(x)$ for which $\displaystyle f([-1,\ 1])=(-\infty,\ \infty)$.

My thoughts: $\displaystyle f(x)=\frac{x}{(x-1)(x+1)}$ is a function for which $f((-1,\ 1))=(-\infty,\ \infty)$.
$$\displaystyle f(x)=\tan \left( \frac{x}{\pi/2} \right), \ \ x\in (-1,1)$$

will map $$(-1,1)$$ to $$(-\infty, \infty)$$ but $$[-1,1]$$ might need a bit more thought, though you can just define $$f(-1)=f(1)=0$$

CB

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